Question 155: Centre of Mass and Rotational Motion

Question

As shown in figure, when a spherical cavity
(centered at O) of radius 1 is cut out of a uniform
sphere of radius R (centered at C), the centre of
mass of remaining (shaded) part of sphere is at
G, i.e, on the surface of the cavity. R can be
detemined by the equation :
![](https://imagex.cdn.examgoal.net/7k9k2k5hgh6qe/54bef7e3-eda0-4432-8ac1-6939226bd27c/ac465f60-38c4-11ea-92dd-4b9c3519996f/file-7k9k2k5hgh6qf-238w.jpg)

Accepted Answer

By concept of COM
m
0
R
0
= m
cavity
R
cavity
$ \Rightarrow $ $\left( {{4 \over 3}\pi {R^3}ho  - {4 \over 3}\pi {{\left( 1 ight)}^3}ho } ight)$ (2 - R) = ${{4 \over 3}\pi {{\left( 1 ight)}^3}ho }$ $ 	imes $ (R - 1)
$ \Rightarrow $ (R
3
Ã¢ÂÂ 1) (2 Ã¢ÂÂ R) = R Ã¢ÂÂ 1
$ \Rightarrow $(R
2
+ R + 1) (2 Ã¢ÂÂ R) = 1
![](https://imagex.cdn.examgoal.net/7kd4dk68qg1wd/3d2b70ef-18af-4134-8f2c-dbc00e9741fd/d18ea4d0-47c4-11ea-b62d-51ccc5d4afb6/file-7kd4dk68qg1we-344w.jpg)

Answer

(R
2
+ R – 1) (2 – R) = 1

Answer

(R
2
– R – 1) (2 – R) = 1

Answer

(R
2
– R + 1) (2 – R) = 1

Answer

(R
2
+ R + 1) (2 – R) = 1

Centre of Mass and Rotational Motion

As shown in figure, when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centered at C), the centre of mass of remaining (shaded) part of sphere is at G, i.e, on the surface of the cavity. R can be detemined by the equation :

Choose the correct answer: